1) This document provides biographical and career information about Cheng-Chin Chiang, including his education, work experience at KEK and NSRRC, and publications. 2) As part of his work at KEK, Cheng-Chin helped with the BELLE experiment to study CP violation and measure properties of B meson decays using an electron-positron collider. 3) At NSRRC, Cheng-Chin has worked on simulation and analysis of beam dynamics for the TPS synchrotron, including optimizing the lattice design and estimating effects like eddy currents during ramping.

1. Simulation and Analysis of
the Data in TPS
2012/10/24
Cheng-Chin Chiang 江政錦
1

2. Personal Data
Present Position:
Assistant Researcher in Beam Dynamics Group, NSRRC
Education:
National Taiwan University (2004~2009), Ph.D. in Physics
Experience:
2004~2010
(1) Member of BELLE collaboration in KEK
(2) On call shift of BELLE sub-detector in KEK
(3) System manger of NTU High Energy Lab.
(4) Internal referee of Physical analysis group in BELLE collaboration
2010~2012
(5) Computer programming for TPS project
2

3. Working Experience at
KEK-BELLE
3

4. KEK Campus (Tsukuba, Japan)
4

5. KEK-BELLE e +e- Collider
• Two separate rings for e+ and e-
• Energy in CM is 10.58GeV  Y(4S)
• Ring length 3Km
8.0 GeV e- Belle
3.5 GeV e+
5

6. KEK e +e- Accelerator
e+/e- Linac
Straight Section
Arc Section
6
e+ Generator of linac
Electron Source of linac

7. The BELLE Detector
Extreme Forward Calorimeter
γ, π0 reconstruction
e+- identification
7

8. My Working Place at KEK
Extreme Forward Calorimeter Electronic-Hut BELLE control room
Spring Autumn Kitty 8

9. Study the CP (Charge × Parity)
Violation
For example: B0→J/ψ K0 Decay -- B0 Decay
(Time dependent CP violation) -- B0 Decay
9

10. The Challenge of CP Violation
• In theoretical calculations:
- We need a good model to explain the behavior of B meson
decays from experimental measurements
Tree diagram Penguin diagram
• In experiment:
- We need to produce the maximum number of B meson decays
for good measurements in statistics (i.e. good luminosity).
- We need good analysis methods and tools to evaluate the
huge amount of experimental data 10

11. : B0 →ρ0ρ0
: Continuum 657 Million BB Data Measurement
: b→c decays
: Other charmless (B0→ρ0ρ0 Decay)
B decays
Mode Yield Eff.(%) Σ BF (x10-6) UL (x10-6)
+23.6+10.1 +0.2
ρ0ρ0 24.5−22.1−16.2 9.16 (fL=1) 1.0 0.4 ± 0.4 −0.3 <1.0 (fL=1)
+67.4 +3.5
ρ0ππ 112.5−65.6 ± 52.3 2.90 1.3 5.9−3.4 ± 2.7 <12.0
4π +61.2+27.7
161.2−59.4−25.1 1.98 2.5 +4.7+2.1
12.4 −4.6−1.9 <19.3
€ +14.5+4.8 €
ρ0f0 −11.8−12.9−3.6 9.81 … … <0.3
€ €
f0f0 +4.7
−7.7−3.5 ± 3.0 10.17 … … <0.1
€ +37.0 € +1.9
f0ππ 6.3−34.7 ± 18.0 2.98 … 0.3−1.8 ± 0.9 <3.8
€
11
€
€ €

12. Publications
1. C.C. Chiang et al. (Belle Collaboration), ``Measurement of B0 → ππππ
decays and search for B → ρ0ρ0”, Phys. Rev. D, 78, 111102(R) (2008);
arXiv:0808.2576.
2. C.C. Chiang et al. (Belle Collaboration), ``Measurement of B0 → ππππ
decays and search for B → ρ0ρ0 at Belle”, in the Book ``Les
Rencontres de physique de la Vallée d'Aoste”, Edited by M. Greco,
ISBN 978-88-86409-56-8, p.365-378 (2008).
3. C.C. Chiang et al. (Belle Collaboration), ``b → d and other charmless B
decays at Belle”, European Physical Society Europhysics Conference
on High Energy Physics (2009), PoS(EPS-HEP2009) 207;
http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=84.
4. C.C. Chiang et al. (Belle Collaboration), ``Search for B0 → K*0 anti-K*0,
B0 → K*0 K*0 and B0 → KKππ decays”, Phys. Rev. D, 81, 071101(R)
(2010); arXiv:1001.4595.
5. C.C. Chiang et al. (Belle Collaboration),``Improved Measurement of the
Electroweak Penguin Process B → Xs l+l-“, 35th International
Conference of High Energy Physics, PoS(ICHEP2010) 231;
http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=120.
12

13. Working Experience at
NSRRC
13

14. Optimize the TPS/BR Lattice
FULL
TPS booster b6p4d2
20. Linux version 8.23/08 28/09/12 10.28.00
10
x y DX10
(m), DX
18.
16.
14.
(a) Baseline Design:
12.
10. Qx= 14.3796, Qy= 9.3020
Cx= 1.0, Cy= 1.0
8.
6.
4.
2.
0.0
0.0 10. 20. 30. 40. 50. 60. 70. 80. 90.
s (m)
E / p0c = 0 .
Table name = TWISS
FULL
TPS booster b6p4d2
20. Linux version 8.23/08 28/09/12 10.28.20
10
x y DX10
(m), DX
(b) From Magnet Group Data:
18.
16.
14.
12.
10.
Qx= 14.3781, Qy= 9.3057
8.
6.
(ΔQx= -0.0015, ΔQy= +0.0037)
4.
2. Cx= 0.95, Cy= 1.25
0.0
0.0 10. 20. 30. 40. 50. 60. 70. 80. 90.
s (m)
E / p0c = 0 .
Table name = TWISS
FULL
TPS booster b6p4d2
20. Linux version 8.23/08 28/09/12 10.28.30
10
x y DX10
(m), DX
18.
16.
14.
(c) New Re-Matching Result:
12.
10.
Qx= 14.3799, Qy= 9.3027
8.
6. (ΔQx= +0.0003, ΔQy= +0.0007)
Cx= 1.0, Cy= 1.0
4.
2.
0.0
0.0 10. 20. 30. 40. 50. 60. 70. 80. 90.
s (m) 14
E / p0c = 0 .
Table name = TWISS

15. Check the Dynamic Aperture (DA) for
TPS/BR with 10 Random Machines
E/E = 0%
14
Blue: baseline lattice (a)
βx=14.926, βy=6.749
1
2
Red: new matched lattice (c)
12 3
4
10
βx=14.904, βy=6.683 5
6
7
8
The multipole field errors are adopted
y (mm)
9
8 10
1
2 in the lattice model.
6 3
4
5
4
6
7 The size of DA is related to the injection
8
2
9
10
efficiency. We do not yet consider the
0
close orbit distortion and orbit variations
-30 -20 -10 0
x (mm)
10 20 30
due to ramping.
E/E = -1.5% E/E = 1.5%
14 14
βx=15.942, βy=5.928 βx=13.898, βy=7.643
1 1
2 2
12 3 12 3
4 4
10
βx=15.928, βy=5.854 5
6
10
βx=13.872, βy=7.577 5
6
7 7
8 8
y (mm)
y (mm)
9 9
8 10 8 10
1 1
2 2
6 3 6 3
4 4
5 5
6 6
4 7 4 7
8 8
9 9
2 10 2 10
0 0
-30 -20 -10 0
x (mm)
10 20 30 -30 -20 -10 0
x (mm)
10 20 30
15

16. Estimate Eddy Current Effect in TPS/BR
The beam is injected from linac The beam energy is increased in
to TPS/BR at 150 MeV TPS/BR from 150 MeV to 3 GeV
(DESY formula) (S.Y. Lee’s formula)
0.2 3 2
K2 (S.Y. Lee) x (S.Y. Lee)
0.18 K2 (SLS) 1.5
y (S.Y. Lee)
Energy 2.5
0.16 1 x (SLS)
y (SLS)
0.14 0.5
2
Chromaticity
Energy (GeV)
0.12
K2 (1/m3)
0
0.1 1.5 -0.5
0.08 -1
0.06 ΔK2(at Dipole) vs. Time 1
-1.5
Chromaticity vs. Time
0.04 -2
0.5
0.02 -2.5
0 0 -3
0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 160
Time (ms) Time (ms)
Check DA for the worst (Eddy) case (at 23 ms)
16

17. Check DA with 100 Random Machines
TPS/BR Original lattice model
E/E = -1.5% E/E = 0% E/E = 1.5%
14 14 14
dynap dynap dynap
chamber chamber chamber
12 12 12
10 10 10
y (mm)
y (mm)
y (mm)
8 8 8
6 6 6
4 4 4
2 2 2
0 0 0
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm)
w/ Eddy effect (worst case)
E/E = -1.5% E/E = 0% E/E = 1.5%
14 14 14
dynap dynap dynap
chamber chamber chamber
12 12 12
10 10 10
y (mm)
y (mm)
y (mm)
8 8 8
6 6 6
4 4 4
2 2 2
0 0 0
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm)
17

18. Apply Sextupole Magnets for Chromaticity
Correction During TPS/BR Ramping
Chromaticity = (+1.07, +1.50)
0 2
K2 (Eddy current effect, DESY formula)
-1 K2 EDDY vs. K2 SD 1 K2 (SD sextupole strength)
K2 (SF sextupole strength)
K2 (SD Sextupole Strength) (1/m^3)
-2
0
-3
-1
K2 (1/m3)
-4
€ -2
-5
’check.log’ u 1:(2.0*$2)
fit result: a1=-28.2654, b1=-0.012603
-3
-6
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
K2 (Sextupole Strength Induced by Eddy Current Effect) (1/m^3)
-4
K2 SD = (−28.2654) × K2 EDDY − 0.0126 -5
K2 (SF, SD) vs. Time
Chromaticity = (+1.07, +1.50)
0.5
’check.log’ u 1:(2.0*$3)
fit result: a2=2.27689, b1=0.00534554 -6
0.45 0 20 40 60 80 100 120 140 160
0.4
K2 EDDY vs. K2 SF Time (ms)
K2 (SF Sextupole Strength) (1/m^3)
(For a ramping period)
0.35
€ 0.3
0.25
0.2
0.15
€ 0.1 MAD Chromaticity (ξx , ξy ) ~ (+1, +1)
0.05
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
K2 (Sextupole Strength Induced by Eddy Current Effect) (1/m^3)
18
K2 SF = (2.2769) × K2 EDDY + 0.0053
€

19. Check DA with 100 Random Machines
w/ Eddy effect (worst case) + sext. corrections
E/E = -1.5% E/E = 0% E/E = 1.5%
14 14 14
dynap dynap dynap
chamber chamber chamber
12 12 12
10 10 10
y (mm)
y (mm)
y (mm)
8 8 8
6 6 6
4 4 4
2 2 2
0 0 0
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm)
In summary, applying sextupole magnets in TPS/BR during the energy
ramping allows us to improve the DA.
19

20. Establish Analysis Tools (MIA&ICA)
• To prepare the analysis tools for TPS commissioning, we apply MIA
(Model Independent Analysis) [1] and ICA (Independent Component
Analysis) [2] in turn-by-turn BPM data mining.
[1] Y. T. Yan et al., Report No. SLAC-PUB-11209 (2005).
[2] X. Huang et al., Phys. Rev. ST Accel. Beams 8, 064001 (2005).
• MIA or ICA are fast analyses (one-shot) for BPM beam signal, which
are used to measure the lattice parameters such as beta, phase
advance, dispersion, betatron and synchrotron tunes.
• We test MIA and ICA methods with TPS/BR simulation data and TLS
/SR experimental data.
• For TPS/BR analysis, we have included the multipole errors, eddy
current effects, and BPM noise in track simulation.
20

21. The Principle of MIA
• We decompose the equal time covariance matrix of turn-by-
turn BPM data with Singular Value Decomposition (SVD):
⎛ x1 (1) x1 (2)  x1 (1000) ⎞
⎜ ⎟
⎜ x 2 (1) x 2 (2)  x 2 (1000) ⎟
For 60 BPMs and 1000 turns: X(t) =
⎜     ⎟
⎜ ⎟
⎝ x 60 (1) x 60 (2)  x 60 (1000)⎠
CX = X(t)X(t)T = UΛU T (decomposed with SVD)
€ ⎛ S1 ⎞ Dx Dispersion
Spatial Temporal ⎜ ⎟
⎜ S2 ⎟
⎜ S3 ⎟ νx Betatron motion
€ ∴ X = U(U X) = ( A1
T
A2 A3 A4 A5 )⎜ ⎟
⎜ S4 ⎟
Dx νx 2νx ⎜ S5 ⎟ 2νx Sextupole terms
⎜ ⎟
⎝  ⎠ 21

22. Extract Beta, Phase, Dsipersion and Tunes from the First
Three of Largest Singular Values
For horizontal betatron motion: Dx = A1 × const.
2 2
⎛ s1 ⎞ βx = (A2 + A3 ) × const.
⎜ ⎟
⎜ s2 ⎟ ⎛ ⎞
−1 A2
X = U(U T X) = ( A1 A2 A3  0)⎜ s3 ⎟
⎜ ⎟
∴ φx = tan ⎜ ⎟
⎝ A3 ⎠
⎜  ⎟
⎜ ⎟
⎝ 0 ⎠ ν syn. = FFT(s1)
⎛ βx1 βx1 ⎞
⎜ aDx1 sin(ν x φ1 ) cos(ν x φ1 ) ⎟ ν x = FFT(s2,3 )
⎜ M M ⎟
⎜ βx 2 βx 2 ⎟
aDx 2 sin(ν x φ 2 ) cos(ν x φ 2 ) ⎟
= ⎜ M M Spatial Matrix
⎜    ⎟
⎜
⎜ aDxm
βxm
sin(ν x φ m )
βxm €
cos(ν x φ m )
⎟
⎟
€
(a = constant, Dx= dispersion)
⎝ M M ⎠
⎛ λ λ1 λ1 ⎞
⎜ 1 sin(2πν syn. • 0) sin(2πν syn. • 1)  sin(2πν syn. • N)⎟
⎜ N N N ⎟
⎜ λ2
cos(2πν x • 0)
λ2
cos(2πν x • 1) 
λ2 ⎟
cos(2πν x • N) ⎟ Temporal Matrix
×⎜ N
⎜ λ
N N
⎟ (νsyn.=synchrotron tune)
λ3 λ3
⎜ 3
sin(2πν x • 0 sin(2πν x • 1)  sin(2πν x • N) ⎟
⎜ N N N ⎟ 22
⎝     ⎠

23. Ramping Effects vs. Turn Number
3
Ramping Energy
9 10 1 6 7 8 9 10
Ramping RF Voltage
Beam Energy 8 5
7 4
2.5
0.8
6 3
RF Voltage (MV)
2
RF Voltage
Energy (GeV)
0.6
1.5 5 2
4 0.4 1
2 3
1 1-10000 turn 1-10000 turn
10001-20000 turn 10001-20000 turn
20001-30000 turn 20001-30000 turn
1
30001-40000 turn 30001-40000 turn
40001-50000 turn 0.2 40001-50000 turn
0.5 50001-60000 turn 50001-60000 turn
60001-70000 turn 60001-70000 turn
70001-80000 turn 70001-80000 turn
80001-90000 turn 80001-90000 turn
90001-100660 turn 90001-100660 turn
0 0
0 20000 40000 60000 80000 100000 0 20000 40000 60000 80000 100000
Turn Number Turn Number
Ramping Sextupole Strength K2
2
SF sextupole strength
1
1 2 3 4 5 6 7 8 9 10 It takes about 100,660 turns
0 to accomplish a ramping cycle.
Eddy current effect, DESY formula
-1
K2 (1/m^3)
-2 Eddy Effect Each color represents
specific ramping period
-3
1-10000 turn
SD sextupole strength 10001-20000 turn
20001-30000 turn
-4
(for every 10,000 turns).
30001-40000 turn
40001-50000 turn
50001-60000 turn
-5 60001-70000 turn
70001-80000 turn
80001-90000 turn
90001-100660 turn
-6
0 20000 40000 60000 80000 100000 23
Turn Number

24. 6-D Phase Space for a Ramping Cycle
X vs. PX Y vs. PY -ct vs. ΔE/E
BPM1 {X-PX} - plane BPM1 {Y-PY} - plane BPM1 {T-PT} - plane
0.0006 0.002
1-10000 turn 1-10000 turn
0.0006 10001-20000 turn 10001-20000 turn
20001-30000 turn 20001-30000 turn
30001-40000 turn 0.0015 30001-40000 turn
0.0004 40001-50000 turn 40001-50000 turn
0.0004 50001-60000 turn 50001-60000 turn
60001-70000 turn 60001-70000 turn
70001-80000 turn 0.001
70001-80000 turn
80001-90000 turn 80001-90000 turn
0.0002 90001-100660 turn 90001-100660 turn
0.0002
0.0005
BPM1
PX/P0
PY/P0
dE/E
0 0 0
-0.0002 -0.0005
.
-0.0002 1-10000 turn
10001-20000 turn
20001-30000 turn
30001-40000 turn -0.001
40001-50000 turn -0.0004
-0.0004 50001-60000 turn
.
60001-70000 turn -0.0015
70001-80000 turn
80001-90000 turn -0.0006
90001-100660 turn
-0.0006 -0.002
-0.003 -0.002 -0.001 0 0.001 0.002 0.003 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0 0.02 0.04 0.06 0.08 0.1
.
X (m) Y (m) -ct (m)
. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
.
.
. Each color represents specific tracking period
(for every 10,000 turns).
BPM60
24

25. Reconstruct TPS/BR Lattice Parameters
with MIA
Reconstructed value at BPM
Model
20 30 20 30
18
(a) (b) 18
(c) (d)
25 25
16
x = 0.380 16
y = 0.302
14 20 14 20
Power (Model: 0.3796) (Model: 0.3020)
Power
(m)
(m)
12 12
15 15
10 10
x
y
8 10 8 10
6 6
5 5
4 4
2 0 2 0
0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5 0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5
s (m) Horizontal Tune s (m) Vertical Tune
0.7 30
(e) (f)
0.6
25 The reconstructed values of βx, βy and horizontal
0.5
20
= 0.025 dispersion Dx at BPMs are shown as red dots in
0.4 s
Power
Dx (m)
0.3 15
(Model: 0.0250)
(a), (c) and (e), respectively. The gray lines are
0.2
10
model values along the TPS booster. The
0.1
5
reconstructed tunes for νx, νy and νs are shown
-0.1
0
0
in (b), (d) and (f), respectively.
0 50 100 150 200 250 300 350 400 450 500 0 0.1 0.2 0.3 0.4 0.5
s (m) Synchrotron Tune
25

26. The Principle of ICA
• We diagonalize the non-equal time covariance matrices of turn-by-
turn BPM data:
⎛ x1 (1) x1 (2)  x1 (1000) ⎞
⎜ ⎟
⎜ x 2 (1) x 2 (2)  x 2 (1000) ⎟
For 60 BPMs and 1000 turns: X(t) =
⎜     ⎟
⎜ ⎟
⎝ x 60 (1) x 60 (2)  x 60 (1000)⎠
whitening
⎛ Λ1 0 ⎞⎛U1T ⎞
CX (τ = 0) = X(t)X(t)T = (U1,U 2 )⎜ ⎟⎜ T ⎟,
⎝ 0 Λ 2 ⎠⎝U 2 ⎠
€
CX (τ k ≠ 0) = X(t)X(t + τ k )T , k = 1,2,3...
The Jacobi-like joint diagonalization is applied to find out a unitary matrix
W which is a joint diagonalizer for all the auto-covariance matrices:
€ s = W T (Λ−1/ 2U1T )X (temporal)
1
⇒ CX (τ k ) = WDkW T ,
A = (Λ−1/ 2U1T ) −1W
1 (spatial)
(k = 1,2,3...) 26

27. Reconstruct TLS/SR Lattice Parameters with ICA
• We practice the ICA in experimental turn-by-turn data for TLS/SR.
• The horizontal and vertical tunes of TLS/SR model are 0.310 and 0.277, respectively;
the horizontal and vertical tunes from measurement are 0.302 and 0.180, respectively.
Horizontal singular values Vertical singular values
36
36
Mode 1: βx Mode 1: βy
34
34
Mode 2: βx Mode 2: βy
32
32
Mode 3: βx There are horizontal betatron
log(SVy)
Mode 3: βy There are vertical betatron
log(SV )
x
30
30
couplings, the magnitude of
couplings, the magnitude of
Mode 5: βy Mode 4: βx coupling is about 10-3 of vertical
28
coupling is about 10-7 of 28
betatron oscillation.
horizontal betaton oscillation.
26
Mode 7: Dx 26
24
24
22
22 0 10 20 30 40 50 60
0 10 20 30 40 50 60
SVx Index SVy Index
25 25 1.4
1.2
20 20
1
Reconstructed value at BPM 15 15
Dx (m)
(m)
(m)
0.8
Model value at BPM
y
x
0.6
10 10
Model 5 5
0.4
0.2
0 0 0
0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120
s (m) s (m) s (m)
27

28. Summary of MIA&ICA
• We have successfully extracted lattice parameters, like beta, phase
advance, dispersion and tunes with MIA or ICA for TPS/BR and TLS
/SR.
• We have included MIA&ICA analysis codes in MATLAB based system.
• The property of MIA&ICA is fast analysis, so we can measure the
machine status within seconds. It is suitable for TPS/BR analysis.
• The MIA&ICA provides another information for LOCO, which would be
helpful in machine measurement and modeling.
28

29. Injection Study for TPS/SR
• In order to reduce the radiation level, we study the tolerance of injected
beam condition
• Use Tracy-II for 6-D tracking. The lattice model includes the injection
kicker strength, septum arrangement, chamber limits, multipole field
errors (10 random machines are used), close orbit distortion and its
correction by applying correctors, etc.
• We generate a thousand particles as a bunch of a beam and track
these particles for a thousand turns
• Check the survival rate of a beam bunch and record the lost information
of particles, including lost position, lost plane and lost turn number.
These information are useful for radiation protection.
29

30. Schematic Layout of TPS/SR Injection
3.6 2.8 3.6
K1 K2 K3 Bumped K4
Stored beam stored beam
0.6 Injected beam
0.6 0.6
0.6
Kicker magnet
0.8
0.8 Unit:(m)
Pulsed septum
DC septum (AC septum)
K3 K4 K1 K2
e-
t1～T0
t0= 0 t1=T0
Injection pt. Injection pt.
30

31. QL1
K1 K2 400 800 K3 K4 QL1
68 mm 54 mm
600 600 [-34, +34] [-20, +34] 600 600
700 3000
1100
1100
3000
700
Middle of R1 straight Injection point
Simplified model for chamber x’
limit used in injection simulations.
Septum wall
The chamber limits in long and 3 mm
short straight sections are: Bumped beam acceptance
[x = ±34 mm, y = ±5 mm] Acceptance
Bumped stored beam
x
Injected beam Stored beam
Beam stay clear = 20.0 mm
Xoffset = 23.8 mm
31

32. Phase Space (Px/P0 vs. x)
Choose one of the random machines and scan injected beam position in horizontal.
4 4 4 4
Xoffset = 23.8 mm Xoffset = 24.8 mm Xoffset = 25.8 mm Xoffset = 26.8 mm
Px / P0 (x10-3)
Px / P0 (x10-3)
Px / P0 (x10-3)
Px / P0 (x10-3)
3 3 3 3
2 2 2 2
1 1 1 1
0 0 0 0
Turn 0 Turn 0 Turn 0 Turn 0
-1 Turn 1 -1 Turn 1 -1 Turn 1 -1 Turn 1
Turn 2 Turn 2 Turn 2 Turn 2
Turn 3 Turn 3 Turn 3 Turn 3
-2 Turn 4 -2 Turn 4 -2 Turn 4 -2 Turn 4
Turn 5 Turn 5 Turn 5 Turn 5
Turn 6 Turn 6 Turn 6 Turn 6
Turn 7 Turn 7 Turn 7 Turn 7
-3 Turn 8 -3 Turn 8 -3 Turn 8 -3 Turn 8
Septum Septum Septum Septum
Septum Septum Septum Septum
-4 -4 -4 -4
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm) x (mm)
4 4 4 4
Xoffset = 27.8 mm Xoffset = 28.8 mm Xoffset = 29.8 mm Xoffset = 30.8 mm
Px / P0 (x10-3)
Px / P0 (x10-3)
Px / P0 (x10-3)
Px / P0 (x10-3)
3 3 3 3
2 2 2 2
1 1 1 1
0 0 0 0
Turn 0 Turn 0 Turn 0 Turn 0
-1 Turn 1 -1 Turn 1 -1 Turn 1 -1 Turn 1
Turn 2 Turn 2 Turn 2 Turn 2
Turn 3 Turn 3 Turn 3 Turn 3
-2 Turn 4 -2 Turn 4 -2 Turn 4 -2 Turn 4
Turn 5 Turn 5 Turn 5 Turn 5
Turn 6 Turn 6 Turn 6 Turn 6
Turn 7 Turn 7 Turn 7 Turn 7
-3 Turn 8 -3 Turn 8 -3 Turn 8 -3 Turn 8
Septum Septum Septum Septum
Septum Septum Septum Septum
-4 -4 -4 -4
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm) x (mm)
4 4 4
Xoffset = 31.8 mm Xoffset = 32.8 mm Xoffset = 33.8 mm
Px / P0 (x10-3)
Px / P0 (x10-3)
Px / P0 (x10 )
3 3 3
-3
2 2 2
1
0
1
0
1
0
Only show 9 turns
-1
Turn 0
Turn 1
Turn 2
Turn 3
-1
Turn 0
Turn 1
Turn 2
Turn 3
-1
Turn 0
Turn 1
Turn 2
Turn 3
Turn 4
Results
-2 Turn 4 -2 Turn 4 -2
Turn 5 Turn 5 Turn 5
Turn 6 Turn 6 Turn 6
Turn 7 Turn 7 Turn 7
-3 -3 -3 Turn 8
Turn 8 Turn 8
Septum Septum Septum
Septum Septum Septum
-4 -4 -4
-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30
x (mm) x (mm) x (mm)
32